Averages problem

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jessicamuniz: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jul 17, 2008 1:02 pm

Averages problem

by jessicamuniz » Sat Aug 09, 2008 3:12 pm

Hi,
Here is a question. The answer is A but I would like to get your point of view with the explanations.
Thanks a lot in advance.

If each of the bowlers in a tournament bowled an equal number of games, what is the average (arithmetic mean) score of all the games bowled in the tournament?
1) Seventy percent of the bowlers had an average (arithmetic mean) score of 120, and the other 30% had an average score of 140.
2) Each of the 350 bowlers in the tournament bowled 3 games.

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Source: Beat The GMAT — Problem Solving | Sat Aug 09, 2008 3:12 pm

beeparoo: Master | Next Rank: 500 Posts; Posts: 200; Joined: Sun Jun 17, 2007 10:46 am; Location: Canada; Thanked: 9 times

Re: Averages problem

by beeparoo » Sat Aug 09, 2008 5:04 pm

jessicamuniz wrote:Hi,
Here is a question. The answer is A but I would like to get your point of view with the explanations.
Thanks a lot in advance.

If each of the bowlers in a tournament bowled an equal number of games, what is the average (arithmetic mean) score of all the games bowled in the tournament?
1) Seventy percent of the bowlers had an average (arithmetic mean) score of 120, and the other 30% had an average score of 140.
2) Each of the 350 bowlers in the tournament bowled 3 games.

STATEMENT 1:
Let b = total number of bowlers
Let SUM(tot) = sum of all scores

Let SUM(A) = sum of the scores of 70% of bowlers
SUM(A)/0.7b = 120

Let SUM(B) = sum of the scores of the rest of the bowlers; the 30%
SUM(B)/0.3b = 140

SUM(tot) = SUM(A) + SUM(B) = 120*(0.7b) + 140*(0.3b)

Avg = SUM(tot)/b = 120*0.7 + 140*0.3 ....SUFFICIENT

Statement 2:
Without any information about the total scores, you cannot calcalate the average score. ....INSUFFICIENT

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